Link Sheets and New Groups

Link sheets are my favorite way to help students connect the four representations of a function. This day I used them to help students find new groups. In my honors classes they had seen Link sheets before, so they knew what they were supposed to look like, but my merit classes hadn’t yet done link sheets, so this activity worked great as an intro to them for link sheets.

The Activity

I cut up the sheets below into quarters. Notice that every link sheet portrays a different function. I pass these quarters out randomly to the class and they have to find “the rest of their link sheet”. Or as I explained in merit (since they hadn’t done link sheets yet) “find the graph that matches your table, or the equation that matches your graph, etc.”.

The students then answered the questions on each link sheet (same answers on each sheet but different questions!), and then glued the four parts together on a blank paper.

I used this to have them randomly find their new groups and seats, though they wouldn’t have to be permanent. Once everyone finished, we did a gallery walk.

Link to documents in case the iframe is broken.

Link to presentation of instruction in case iframe is broken.

The Result

Most of the students found their groups after some struggle (yay!). I wasn’t prepared for some students getting it wrong; there was one group in each of my merit classes who sat down with the wrong group, so of course there were people walking around looking for their group when their group had sat down already! A quick remedy of this is to simply check in with every group as they sit down. It took me longer than it should have because I was ready for students to be confused, but wasn’t ready for students to be confident in the wrong answer. Don’t assume that students will check each other’s work!


Here’s a completed link sheet.


They should have labeled the point on the graph, too.


One great thing about this lesson is that I got another day out of the materials, while having the students dig deeper! Because every group only saw one link sheet (their own), I gave them a blank link sheet (last page of the document above) and one slice or quarter[1] of another group’s link sheet. They had to fill out the other three parts with their group.

Once they completed it having started with the description quarter, then I gave them a different quarter as a starting point. With each of the non-description quarters, they had to write a description of a situation that matched the function, which many of them enjoyed! I even motivated one student by talking him through his interests and pointing out that he can write a linear function based on how many youtube videos he creates of his bottle-flipping.

I printed the blank link sheet front and back on two sheets so that they would have four link sheets, one starting from each quarter, by the time they were finished.

This whole lesson and extension took two 47 minute periods in honors, who had taken notes about link sheets previously. Homework the second day was “finish the link last link sheet” but most of the students finished it in class already.

In merit, we did notes as well, so over the two days they were only able to fill out two link sheets in their groups (starting with 2 of the 4 quarters).

Checking Their Work



Another good thing about this is I taped up the completed link sheets from the first activity (that had been glued together) and students were able to check their work as they completed each link sheet by walking around the room and finding the same link sheet.


[1] For merit I modified it to begin with two slices or quarters.


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[DITL] September 22nd

6:05 am

I wake up to my phone alarm (my back-up alarm) for the first time this year. Guess I’ve been “thinking about too much” this year to get a really good night’s sleep.


7:00 am

After getting ready, I’m driving to work. Only a ~10 minute commute.

7:10 am

I get to school and begin getting ready. Today is a half-day (end of mid-term/quarter) so there’s no ELT (homeroom). Here’s schedule. (I only put up my classes, 3rd – 7th pd.)


9:20 am

The morning has flown by, but I got organized and was proud of how “ready” each of the things on my desk were. See photos.



Also had the agendas ready. I’ve been better about that this year.


10:36 am

3rd and 4th periods went pretty smoothly (you can see the agenda for a synopsis). I’m really excited to be using Pear Deck and I hope I am able to get it ready for many future lessons.

I announced the winners of the “Amazing Amusement”, my weekly challenge, and I made the girl in 4th period excited. When you win my weekly challenge, you get to a bag of fruit snacks (no candy allowed at our school) and you get to put your name on the Wizard Wall. I’d show you a picture of it, but it has student names on it. Here’s the winner’s work (shortest, most accurate route).


Unfortunately the 6th period student wasn’t in school today, but she does read my blog so maybe she’ll find out she won right here!

For 5th period (Algebra) I got a short 3-act lesson on taxis ready and, though we didn’t finish it, the students enjoyed using the VNPS (whiteboards on the walls). See photos.





And the results of their work:


1:00 pm

The bell rings for the end of the day and I’m a little frustrated at my 7th period because they began putting up chairs and packing up with 2 minutes left while I was showing a video (meat-o-morphosis intro to functions). Well, I guess I should have known: the end of a short day before a long weekend.

4:30 pm

I’m typing up this post because I really want to get home so we can head to the beach! I’m not nearly ready for Monday yet, but I’ll bring grades with me to the beach and hopefully, despite not having internet, I’ll get some work done in preparation for Monday. Where did the last three and a half hours go?!? At least my room is somewhat clean.


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[MTBoS Blaugust] Algebra Properties Discovery Lesson

I want my Algebra 1 class to go as fast as possible, yet I also want them to use generation, a la “Make It Stick”[1], as much as possible. So in the middle of the night, when I couldn’t sleep, I came up with this idea.


Generation is the idea of making students struggle with something before you show them how to do it. I’m not really sure yet how much these Algebra I students have learned before this year, so I hope this’ll make it interesting for those kids who already knew it but are seeing it “from a different angle”.

The google slides should be self-explanatory[2].

(Link in case iframe is broken)

Reasons why I like this approach more than what I’ve done in the past:

  • Generation: students deciding for themselves which properties work for which operations.
  • Collaboration (and they’re using whiteboards hanging on the walls)
  • Cross-curricular: taking English definitions and applying those ideas to math concepts.
  • Mistake correcting: students have to explain why certain properties don’t work, which will (hopefully) reduce how much they make that mistake later.


[1] I still haven’t read the book, but I’ve read so much of what others have said about it, that (1) I really want to read the book and (2) I feel like I’m beginning to understand many of the ideas mentioned in the book.

[2] If they’re not, please tell me because I need to tell my students! 🙂

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[MTBoS Blaugust] The Cover Sheet

I like for students to use cover sheets, but the reason for students can look, on the surface, as rather selfish: “don’t steal my answers!” However, one year I figured out an explanation that makes taking out your cover sheet an altruistic measure.


I’ll type this as a dialogue since that’s the easiest way for me to explain it.

Me: Hey class, I want you to pull out a cover sheet, but does anyone know why we use a cover sheet?

Student: So people don’t CHEAT!

Me: Yes, but there’s another reason. Do you guys ever zone out while thinking or taking a quiz or a test? You know, you’re not really look at the thing where your eyes are pointing? So what if you just zoned out looking at a neighbor’s desk? I can’t see inside your head, so I don’t know that you’re not actually looking at where your eyes are pointing and in that case I would have to assume the worst. We’d have to have a chat after class, probably phone call or email home, and I don’t want to have to do that and I’m sure you don’t. However, if your neighbor had all of their answers covered up, then no-harm-no-foul. You’d be safe and we wouldn’t have to call home. So do you get it when I say “Please take out your cover sheets for your neighbor’s sake”? Nod if you’re with me on that.

*Most students nod*

Me: So please take out a cover sheet for your neighbor’s sake…

Today I had one girl afterwards explain to me that “she zones out looking at the wall, so she’s safe.”

I like how we’ve built up a sense of “we’re in this together, so let’s help each other out” in the classroom, and asking students to take out cover sheets almost feels like a pull in the opposite direction. So I like this explanation because it changes something simple, like a cover sheet, into another way for you to help the people around you.

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[MTBoS] Day 4 of a New Year

Day 4 has been the best day yet. I’m really starting to see the students “get it”[1] when it comes to the Visual Pattern math talks, and we’re only 4 days in!!


Here’s a picture that sums up where we are:


Work is underway!

This picture is a good summary for several reasons:

  • I got a ticket out done in every class today! (Progress, wohoo!)
  • The Green means “Got it!” while the pink means “Need help!”. Blue and Yellow are in between.
  • Therefore many students get it, but several have a ways to go.
  • This “Ticket Out” display still has a ways to go: I have to put the meaning of each color somewhere!
  • The Ticket Outs are part of my big personal goal this year, and therefore this is meaningful in a lot of ways. I realized in the past that I’ve hesitated to collect some kind of formative assessment because then I might have to change what I’m doing. Reading (browsing) them all is enough extra work: changing my plans on top of that is even more! However, I’ve come to realize that this is one of the characteristics of good teaching: understanding the students well enough to adapt your teaching frequently. Recognizing that I didn’t want to put that much time in to adapt was a huge hurdle for me and one of the things that has helped me to actually have students do (and collect and read them). Each following day I try to read some and point out good answers and good mistakes (anonymously for the mistakes), and I think it impresses upon the students that I read these and care that they get it.

I’m excited for this year and we’re only 1 week in!


[1] Mostly because of a few that shout “I get it!!!” in the middle of our discussion.



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[MTBoS Blaugust] First Day!

I’m supposed to do a play-by-play of my entire day today, but it’s late and I need sleep more than I need the recap, so brief, brief recap to help me remember this later.


Got there at 7am, but felt like students were walking in the door 2 minutes later (it was really 8:00am, but oh well). Had 2 hours with “homeroom”, but finished all the things we were supposed to do in ~45 minutes. Oops. Fortunately I know a thing or two about having extra time, so I drew chomp on the board and we played for an hour. The kids loved it and I felt good about getting them to do logical thinking without knowing it.

After 2 fast planning periods, I pulled off my first day pretty well. I need to get clearer on my instructions, especially for the merit classes, but once everyone gets into the rhythm of warm-ups and ticket outs, they’ll all run much more smoothly.

That’s it for now, on to day 2!

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[MTBoS Blaugust] Informal Lesson Plans

It’s been years since I’ve written/typed a formal lesson plan. I often would use Google Calendar to plan the day out (since it’s so easy to add, edit and move things around) and/or use the whiteboard where I write the day’s/week’s “agenda” to mentally go through each day. So I was a little nervous with my principal asked for a “weekly plan” sent to her before the week began.


However, as I began working on it, I realized that this forced me to think through the details that I so often overlook. I was very glad of the exercise and think it was time well spent.

I’d like to share those plans here. Several documents I’ve created/stolen are linked here, so I’d like to give credit to those sources. Thanks to Fawn Nguyen for the visual patterns and ideas for warm-ups all 5 days.  Thanks to Alex Overwijk for the 26 squares idea. Thanks to Julie Reulbach and NCTM Illuminations for the Cheez-it rational approximation of the irrational root idea. Thanks to my co-workers for fleshing out some ideas with me and making these more palpable. I’m sure there’s still some work to be done on these.

(Link in case iframe doesn’t work)

Please give me feedback on my informal lesson plans!

One request for ideas: what do people do early in the year when students are finishing quizzes at different times? I don’t have a good idea for Friday yet.  Thanks!


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